## Select Exercises for Young Proficients in the Mathematicks: Containing I. A Great Variety of Algebraical Problems with Their Solutions. II. A Choice Number of Geometrical Problems with Their Solutions Both Algebraical and Geometrical. III. The Theory of Gunnery, Independent of the Conic Sections. IV. A New and Very Comprehensive Method for Finding the Roots of Equations in Numbers. V. A Short Account of the Nature and First Principles of Fluxions |

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Page 31 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.

Page iv - This man, to his profeffion of an itinerant merchant, had joined the more profitable one of a fortune-teller, which he performed by means of judicial aftrology. Every one knows with what regard perfons of fuch a...

Page xix - Jones, esq. he was, in 1743, appointed professor of mathematics, then vacant by the death of Mr. Derham, in the Royal academy at Woolwich ; his warrant bearing date August 25th. And in 1745 he was admitted a fellow of the Royal Society, having been proposed as a candidate by Martin Folkes, esq. president, William Jones, esq. Mr. George Graham, and Mr.

Page xv - Investigation of a very exact Method or Rule for finding the Place of a Planet in its Orbit, from a correction...

Page xvii - ... that subject, a copy of which Mr. Simpson afterwards received as a present, and found in it the same things demonstrated, to which he himself had directed his enquiry, besides several others. The facility of the method Mr. Simpson fell...

Page xv - Ward's circular Hypothesis, by Means of certain Equations applied to the Motion about the upper Focus of the Ellipse. By this Method the Result, even...

Page 40 - From two places at a distance of 320 miles, two persons, A and B, set out at the same time to meet each other. A travelled 8 miles a day more than B, and the number of days in which they met was equal to half the number of miles B went in a day. How many miles did each travel, and how far per day ? 20.

Page v - These two questions, being at that time pretty difficult ones, show the great progress he had even then made in the mathematics ; and from an expression in the first of them, viz, where he mentions his residence as being in latitude 52°, it appears he was not then come up to London, tin ugh he must have done so very soon after.

Page xvi - ... manner. But what may perhaps best recommend this excellent tract is, the application of the general equations, thus derived, to the determination of the lunar orbit. According to what Mr. Simpson had intimated at the conclusion of his Doctrine of Fluxions, the greatest part of this arduous undertaking was drawn up in the year 1750. About that time M. Clairaut, a very eminent mathematician of the French Academy, had started an objection against Newton's general law of gravitation.

Page vi - Englifh author who had written ' on the fubjcct, except Mr. Hayes ; and his work being a folio, and then pretty fcarce, exceeded his ability of purchafing : however, an acquaintance lent him Mr. Stone's Fluxions, which is a tranflation of...